The present invention relates to a method for designing a diffractive lens that has a combination of a plurality of functions such as beam converging, beam separating and aberration correcting.
Holography technology has been used for designing the diffractive lens that has functions of beam converging and beam separating. For Instance, a diffractive lens that converges a light beam from a light source into three focusing points can be made by recording interference pattern between light from a point corresponding to the light source and divergent light from points corresponding to the three focusing points into a hologram plate. The interference pattern is formed by the interference of actual light wave or computer simulation. The hologram plate converges the light from the same light source into the three focusing points.
A phase function method is known to design a diffractive surface having a beam converging function and an aberration correcting function. In this method, additional optical path length added by the diffractive surface is represented as a mathematical function of a position on the surface. The aberration can be corrected by adjusting coefficients of the function.
However, since it is difficult to control the light amount distribution at the respective focusing points for the holograph technology, it cannot be used for designing a diffractive lens that separates a light beam into equal portions for the respective focusing points.
On the other hand, since the phase function method evaluates aberration of only one diffractive order light, it cannot determine the surface shape when the diffractive surface has the beam separating function.
In general, a lens design requires an evaluation method to optimize the lens characteristics. Many evaluation methods running on the computer have been developed for a refractive optical system, and they can be utilized in the design of a diffractive lens when the diffractive lens has a single optical function. For instance, the ultra high index method using Sweatt model is able to design the optical system Including a diffractive lens by lens design computer programs developed for refractive optical systems.
However, the evaluation methods of the lens design computer programs cannot evaluate the diffractive lens having a combination of a plurality of optical functions, which increases difficulty of the diffractive lens design.
It is therefore an object of the present invention to provide a method for designing a diffractive lens, which is effective for designing a diffractive lens having a combination of a plurality of functions such as a combination of beam converging, beam separating and aberration correcting functions.
For the above object, according to the present invention, there is provided a method for designing a diffractive lens having a combination of a plurality of optical functions, which includes:
defining an expression of each of a plurality of diffractive surfaces, the plurality of diffractive surfaces having the plurality of optical functions, respectively; and
superimposing the defined expressions of the plurality of diffractive surfaces to determine a shape of the diffractive lens, a diffractive lens formed to have the shape having the combination of the plurality of optical functions.
With this construction, each of the diffractive surfaces has a simple optical function and the diffractive lens can be considered as an optical system having the plural diffractive surfaces, which enables evaluation, such as ray tracing, by lens design computer programs developed specifically for a refractive optical system. Thus, the diffractive lens having a combination of a plurality of optical functions can easily be designed. The method according to the present invention is particularly effective for designing a diffractive lens having a beam converging function, a beam separating function and an aberration correcting function.
The expression of each diffractive surface is defined as phase distribution or an actual shape, i.e., distribution of a thickness along an optical axis direction.
In particular, according to the present invention, there is provided a method for designing a diffractive lens that separates an incident light beam into a plurality of beams and condenses the respective separated beams, which includes:
defining an expression of a diffractive surface having a beam converging function based on given focal length;
defining an expression of a diffractive surface having a beam separating function that separates a light beam into plural orders of diffractive light based on said given focal length, a given number of separated light and a given distance between focusing points;
superimposing the defined expressions of the diffractive surface having the beam converging function and the diffractive surface having the beam separating function to determine a shape of the diffractive lens having a combination of a plurality of optical functions.
The superimposing step preferably includes:
calculating a first phase distribution by mapping decimal parts of an optical path difference function, which is expressed in the unit wavelength and represents the defined expression of the diffractive surface having the beam separating function, on a reference phase pattern that represents a variation of phase shifting amount within one pitch to separate a light beam into a plurality of equal portions;
calculating a second phase distribution that corresponds with decimal parts of an optical path difference function, which is expressed in the unit wavelength and represents the defined expression of the diffractive surface having the beam converging function; and
calculating the shape of the diffractive lens by superimposing the first and second phase distributions and converting the superimposed result into the actual shape.
The actual shape of the diffractive surface may have a plurality of concentric rings each of which has a wedge sectional shape. The first and second phase distribution represent the entire area of the diffractive surface including the plural rings, while the reference phase pattern defines the variation of the phase shift amount within the single ring. The reference phase pattern can be predetermined based on the given number of separated light and the given distance between focusing points.
Further, the method may include a step for defining an expression of a diffractive surface having an aberration correcting function that corrects aberration at the respective focusing points caused when the diffractive surfaces having the beam converging function and the beam separating function are superimposed. In such a case, the expressions of the diffractive surfaces having the beam converging function, the beam separating function and the aberration correcting function are superimposed in the superimposing step to define the final shape of the diffractive lens.
The diffractive surface having the aberration correcting function is preferably defined to correct at least coma. The diffractive surface may further correct astigmatism and/or curvature of field.